Does a differential evolution algorithm mutate its population during a generation?
Quoting the original paper:

For each target vector $x_{i,G}$ ,a mutant vector is generated according to
$$ v_{i,G+1} = x_{r_1,G} + F\left(x_{r_2,G} + x_{r_3,G}\right)$$

And later

To decide whether or not it should become a member of generation $G + 1$, the trial vector $v_{i,G+1}$ is compared to the target vector $x_{i,G}$ using the greedy criterion.

I'd say it is pretty unambiguous that author's intent was to split evolving agents' populations into &quot;generations&quot; indexed by $G$. A new generation $G+1$ is created by applying the DE algorithm to the previous generation $G$. No agents are changed within the generation $G$.
So, it looks like the answer to your question is &quot;no&quot; - the population of the current generation $G$ is not mutated. Your second approach is the correct one.